class Solution {
public:
    vector<vector<int>> matrixBlockSum(vector<vector<int>>& mat, int k) {
        int m=mat.size();
        int n=mat[0].size();
        vector<vector<int>> arr(m,vector<int>(n));
        vector<vector<int>> dp(m+1,vector<int>(n+1));
        for(int i=1;i<=m;++i)
        {
            for(int j=1;j<=n;++j)
            {
                dp[i][j]=dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1]+mat[i-1][j-1];
            }
        }

        for(int i=0;i<m;++i)
        {
            for(int j=0;j<n;++j)
            {
                int x1=0,x2=0,y1=0,y2=0;
                x1=max(0,i-k)+1;
                y1=max(0,j-k)+1;
                x2=min(m-1,i+k)+1;
                y2=min(n-1,j+k)+1;
                arr[i][j]=dp[x2][y2]-dp[x1-1][y2]-dp[x2][y1-1]+dp[x1-1][y1-1];
            }
        }
        return arr;
    }
};
